User:BudjarnLambeth/1ed237.8c

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1ed187/163

2ed187/163 →

Prime factorization	n/a
Step size	237.8 ¢
Octave	5\1ed187/163 (1189 ¢)
Twelfth	8\1ed187/163 (1902.4 ¢)
Consistency limit	10
Distinct consistency limit	4
Special properties	Highly composite

1 equal division of 237.8¢ (1ed237.8c), also known as arithmetic pitch sequence of 237.8¢ (APS237.8¢), is an equal nonoctave scale generated by making a continuous chain of intervals of exactly 237.8¢. It is almost exactly 8edt, but retuned to have a slightly more acceptable pseudo-octave. It could be seen as a compromise between 8edt and 5edo, though leaning heavily towards 8edt.

Harmonics

Approximation of harmonics in 1ed237.8c

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.00	+0.44	-22.00	+67.29	-10.56	-39.63	-33.00	+0.89	+56.29	-108.72	-21.56
	Relative (%)	-4.6	+0.2	-9.3	+28.3	-4.4	-16.7	-13.9	+0.4	+23.7	-45.7	-9.1
Step		5	8	10	12	13	14	15	16	17	17	18

5edo, 8edt, 14ed7 for comparison:

Approximation of harmonics in 5edo

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0	+18	+0	+94	+18	-9	+0	+36	+94	-71	+18
	Relative (%)	+0.0	+7.5	+0.0	+39.0	+7.5	-3.7	+0.0	+15.0	+39.0	-29.7	+7.5
Steps (reduced)		5 (0)	8 (3)	10 (0)	12 (2)	13 (3)	14 (4)	15 (0)	16 (1)	17 (2)	17 (2)	18 (3)

Approximation of harmonics in 8edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11	+0	-23	+67	-11	-40	-34	+0	+55	-110	-23
	Relative (%)	-4.7	+0.0	-9.5	+28.0	-4.7	-17.0	-14.2	+0.0	+23.3	-46.1	-9.5
Steps (reduced)		5 (5)	8 (0)	10 (2)	12 (4)	13 (5)	14 (6)	15 (7)	16 (0)	17 (1)	17 (1)	18 (2)

Approximation of harmonics in 14ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3	+23	+6	+101	+26	+0	+9	+46	+104	-61	+29
	Relative (%)	+1.3	+9.6	+2.6	+42.1	+10.9	+0.0	+3.9	+19.2	+43.4	-25.2	+12.2
Steps (reduced)		5 (5)	8 (8)	10 (10)	12 (12)	13 (13)	14 (0)	15 (1)	16 (2)	17 (3)	17 (3)	18 (4)

Intervals

Degree of 1ed65c	Cents Value
0	0
1	237.8
2	475.6
3	713.4
4	951.2
5	1189.0
6	1426.8
7	1664.6
8	1902.4